Notes On Laws of Exponents - CBSE Class 7 Maths
Multiplication of Powers with the Same Base When numbers with the same base are multiplied, the power of the product is equal to the sum of the powers of the numbers. If 'a' is a non-zero integer, and 'm' and 'n' are whole numbers then, am × an = am+n. Division of Powers with the Same Base When numbers with the same base are divided, then the power of the quotient is equal to the difference between the powers of the dividend and the divisor.  If 'a' is a non-zero integer, and 'm' and 'n' are whole numbers then, am ÷ an = am-n. Power of a Power If 'a' is any non-zero integer, and ‘m’and ‘n’ are whole numbers then, (am)n = amn. Multiplication of Powers with the Same Exponent If 'a' is any non-zero integer, and ‘m’ is a whole number then, am × bm = (ab)m. Division of Powers with the Same Exponent If a and b are any non-zero integers and m is a whole number then, am ÷ bm = ($\frac{\text{a}}{\text{b}}$)m. Numbers with an Exponent of Zero For any non-zero integer a, a0 = 1.

#### Summary

Multiplication of Powers with the Same Base When numbers with the same base are multiplied, the power of the product is equal to the sum of the powers of the numbers. If 'a' is a non-zero integer, and 'm' and 'n' are whole numbers then, am × an = am+n. Division of Powers with the Same Base When numbers with the same base are divided, then the power of the quotient is equal to the difference between the powers of the dividend and the divisor.  If 'a' is a non-zero integer, and 'm' and 'n' are whole numbers then, am ÷ an = am-n. Power of a Power If 'a' is any non-zero integer, and ‘m’and ‘n’ are whole numbers then, (am)n = amn. Multiplication of Powers with the Same Exponent If 'a' is any non-zero integer, and ‘m’ is a whole number then, am × bm = (ab)m. Division of Powers with the Same Exponent If a and b are any non-zero integers and m is a whole number then, am ÷ bm = ($\frac{\text{a}}{\text{b}}$)m. Numbers with an Exponent of Zero For any non-zero integer a, a0 = 1.

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